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Sagot :
System of Equations
We use the following variables to solve this problem:
x = number of gallons of 70% antifreeze
y = number of gallons of 30% antifreeze
We need to make 100 gallons of antifreeze, thus:
x + y = 100 [1]
The 100 gallons should be 45% of concentration, thus:
70x + 30y = 100*45
Operating and dividing by 10:
7x + 3y = 450 [2]
From [1]:
x = 100 - y [3]
Substituting in [2]:
7(100 - y) + 3y = 450
Operating:
700 - 7y + 3y = 450
700 - 4y = 450
Subtracting 700:
-4y = -250
Multiplying by -1:
4y = 250
Dividing by 4:
y = 250/4
y = 62.5
From [3]:
x = 100 - 62.5
x = 37.5
We should use 37.5 gallons of 70% antifreeze and 62.5 gallons of 30% antifreeze to get 100 gallons of 45% antifreeze
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